I'm obviously dating up, because I can't figure out what my girlfriend wants me to buy her for Christmas. When I asked her what she wanted, she gave me the three puzzles below. The only hint she gave me is that she only wants one item.

A few things that might help:
She's really lucky. (I mean she is dating me.)
She likes card and board games. (Setters of Catan is her favorite. No, it's not that. She already has it. And 5 expansions, but that's probably not helpful)
She likes animals (especially dogs and cats) and had a cat named Ralph and a dog named Bingo
Her favorite song is that double rainbow song.

The three sub puzzles are obviously needed to solve the puzzle as a whole. The other 'hints' may or may not be helpful after the sub puzzles are solved. On the other hand, the hints (or parts of them) could just be there to distract from the real solution.

$\begingroup$(1) If you can’t figure out what your girlfriend wants, no conclusions can be drawn from this. You could be dating up, down, or sideways. (2) If she’s dating down with somebody who doesn’t understand her, how is she lucky? Is the bit about luck an actual clue, or just egotism? (3) I don’t know what “that double rainbow song” is. Seriously. If this is an actual hint, can you please be more explicit? If we need to guess what song you’re talking about, the question should probably be tagged [knowledge] or [trivia].$\endgroup$
– Peregrine RookDec 24 '16 at 19:36

4 Answers
4

If I can resurrect this one, I think I've spotted the links between all the previous partial solutions, worked out an element that had been missed by all, and can explain the additional hints in the text. Your girlfriend wants you to buy her:

Exploding Kittens, the card game

Puzzle 1 (solved by @PeregrineRook):

Is a Mastermind puzzle, which produces the answer TACO.

Puzzle 2 (solved by @ThirupathiThangavel):

Is a simple word puzzle, which produces the answer WATERMELON.

Puzzle 3 (worked on by @Techidiot with a comment that came very close from @GarethMcCaughan):

Part 1 actually translates via rot-1 as 'I am one thing made of many. I'm very manly but I prefer men.'
Part 2 translates via rot-25 as 'Whenever people discover me I always grow on them. If I become colorless, wisdom comes.'
These clues lead to the answer BEARD:I am one thing made of many. - One beard is made of many hairs.I'm very manly but I prefer men. - A beard is considered a manly thing to have; it 'prefers' men in the sense that it's usually men it grows on.Whenever people discover me I always grow on them. - A beard quite literally grows on a person...If I become colorless, wisdom comes. - Grey hair (or a grey beard) is a sign of age and 'wisdom comes with age'.

However, there was an extra clue hidden in the bold and italicised letters of Puzzle 3 which nobody spotted (because nobody was looking for it):

The letters produced by the rot operations on the bold letters give: AHYIRUPSD, which anagrams to 'HAIRY SPUD'. Since 'spud' is another word for 'potato' this leads to the answer HAIRY POTATO (don't see it yet? Bear with me!).
Meanwhile, the letters produced by the rot operations on the italicised letters give: EDNREREGRHI, which anagrams to 'RED HERRING' and has no further utility for the puzzle!

Why do these lead to the answer above? Because:

4 of the 5 types of 'cat card' in the original game are called TACOCAT (pleasingly palindromic), CATERMELON, BEARDCAT and HAIRY POTATO CAT.

There were other clues in the preamble too:

1. She's really lucky - Exploding Kittens game is partly a game of chance, in the way the deck is shuffled and hands are dealt.
2. She likes card and board games - It's a card game.
3. She likes animals (especially dogs and cats) - It's all about cats!
4. She had a cat named Ralph - The fifth 'cat card' in the game is called the RAINBOW RALPHING CAT.
5. Her favorite song is that double rainbow song - Again, as per 4.

The other answers between them each had one component of the final solution. Hopefully this finally now brings them all together in totality with the fourth previously unspotted one, and you can get down to the shops PRONTO! Here's hoping your girlfriend is a VERY patient woman ;-)

Mastermind, a guessing game a little like hangman
except you guess the entire sequence1 all at once.
Your adversary (i.e., the controller of the game)
responds with how many symbols you have right,
and how many of them are in the right position.
Some implementations always give you $n$ responses,
even though the last $n-2$ are undefined and are always given as zeroes.
So,
$\begin{align}\texttt{CARE}&&2100\end{align}$
tells us that (exactly) two of the letters C, A, R and E are correct
(in the word to be solved), and one of them is in the right position.
Not much to go on.
$\begin{align}\texttt{RACE}&&2200\end{align}$
tells us that two of the letters R, A, C and E are correct —
but we already knew that, since these are the same letters we had before.
The new information is that
both of the correct letters are now in the right positions.
This means that one of the letters that was in the wrong position in CARE
is now in the right position.
From that we can conclude that either A or E is in the right position
(and the other is not in the word at all),
and likewise for R and C (as positioned in RACE).
$\begin{align}\texttt{TARE}&&2200\end{align}$
No change in the information about A and E.
This tells us that either T or R is in the right position
(as positioned in TARE), and the other is not in the word at all.
But we already know that R does not belong in the third position,
so it must not be in the word at all, and T must be the first letter.
This narrows it down to TAC_ (where the _ is not E or R)
or T_CE (where the _ is not A or R).
$\begin{align}\texttt{TORE}&&2100\end{align}$
tells us that we still have two correct letters,
but now only one of them is in the right position.
Well, we know that T is the first letter.
If E is in the word at all, it is in the last position,
so it must not be in the word at all, and we must have TAC_.
But we do have two correct letters,
so the O must be in the word, but just not in the second position.

$\begingroup$3:2 sounds like it might possibly be hair. (White hair is "really" colourless; thin fibres of glass with a matt surface would have a similar appearance. Having white hair is a sign of age. Almost everyone has hair, though "always" seems like an overstatement if this is right.)$\endgroup$
– Gareth McCaughan♦Dec 24 '16 at 23:21

$\begingroup$@Gareth- I'm not sure if it's riddle. May be we need to get the bold & italic letters from these lines and perform operations. Will look into this tommorow(in case if it remains unsolved)$\endgroup$
– TechidiotDec 25 '16 at 5:58

$\begingroup$Combining my answer to Puzzle 1, the clear text of Puzzle 2, and Gareth McCaughan’s response to the interim solution to Puzzle 3 Part 2, we seem to be heading in the direction of this (hover). ROT13 version: ungf -- fcrpvsvpnyyl, Jvagre Onfu ungf.$\endgroup$
– Peregrine RookDec 28 '16 at 22:27